Cameron said he authorised the rescue attempt on Friday afternoon, after becoming increasingly concerned about the safety of Ms Johnston and her colleagues from Medair, a humanitarian non-governmental organisation based near Lausanne, Switzerland.

Helen Johnston was rescued by British soldiers on Friday

He said all four hostages were rescued safely, no British troops were injured and a number of Taliban and hostage-takers were killed.

"It was an extraordinarily brave, breath-taking even, operation that our troops had to carry out," he said.

"I pay tribute to their skill and dedication."

Speaking outside 10 Downing Street on Saturday, the Prime Minister said the rescue should serve as a warning to terrorists across the world who take British citizens hostage.

"They should know if they take British citizens as hostage we do not pay ransoms, we do not trade prisoners.

"They can expect a swift and brutal end."

Cameron said decisions on rescue attempts were "extraordinarily difficult" and "never rushed into". But he said he decided the risks to the workers' lives were getting greater. He added he had spoken Ms Johnston's parents and brother, and the aid worker herself.

"They are incredibly relieved about what has happened. "It's just a huge joy that they are finally going to be re-united and they are all healthy and all well."

He said the rescue involved a number of British troops, helped by ISAF forces as well the Afghan government, and involved a "long route march" without being discovered.

Paying tribute to British troops, he said: "Above all, on this weekend of all weekends, we should say a enormous thank you to the incredibly brave forces that took part in this operation.

"We will never be able to publish their names but the whole country should know we have an extraordinary group of people who work for us who do amazingly brave things."

He added: "This weekend we're going to remember and commemorate 60 years of extraordinary work by Her Majesty the Queen and this weekend we can also remember the frankly incredible work that people who serve in her name do on our behalf all the time."

A statement from Ms Johnston's parents Philip and Patricia and brother Peter said they were "deeply grateful" to her rescuers.

"We are delighted and hugely relieved by the wonderful news that Helen and all her colleagues have been freed," they said.

"We are deeply grateful to everyone involved in her rescue, to those who worked tirelessly on her behalf, and to family and friends for their love, prayers and support over the last twelve days.

"We greatly appreciate the restraint shown by the media since her abduction, and ask that they continue to respect our privacy at this special time."

The aid workers were abducted by a group of armed men during a visit to relief project sites in Badakhshan, Medair said.

Since the kidnapping, the charity kept a lid on publicity which it felt could jeopardise efforts to secure a release.

Spokesman Aurélien Demaurex said the aid workers would now be reunited with their families.

"We are really, really happy," he said.

"Medair is relieved that our colleagues are safe. We are immensely grateful to all parties involved in ensuring their swift and safe return.

"The staff members are on their way to be reunited with their families. We ask the media to respect the need for the privacy of our employees and their families.

"Medair would like to thank everyone for their encouragement and support during this very difficult period. We are also very grateful for the overwhelming messages of support from local Afghan communities."

According to its website, the organisation has worked in Afghanistan since 1996, providing relief to vulnerable and isolated communities.

Despite recent events, a spokesman said the charity was committed to continuing its work "which relies on us working safely within local communities, wherever they may be".